A note on -ultrafilters and -points
A number-theoretic conjecture and its implication for set theory.
A partition theorem for α-large sets
A polarized partition relation and failure of GCH at singular strong limit
The main result is that for λ strong limit singular failing the continuum hypothesis (i.e. ), a polarized partition theorem holds.
A proof (involving Martin's axiom) of a partition relation
A propos des distances entre ensembles de parties
Soit un ensemble fini. Nous nous proposons ici d’établir des indices de distance entre les divers ensembles de parties de . Nous généraliserons pour cela, à , la notion de fonction caractéristique bien connue dans .
A remark on a paper by Karel Prikry
A Remark On Filter Regularity
A remark on filter regularity.
A rigid Boolean algebra that admits the elimination of Q21
Using ♢ , we construct a rigid atomless Boolean algebra that has no uncountable antichain and that admits the elimination of the Malitz quantifier .
A set-theoretical equivalent of the prime ideal theorem for Boolean algebras
A solution of a problem of B. Rotman
A solution of a problem of B. Rotman
A theorem on almost disjoint sets
A Theorem on Directed Quasi-Ordered Sets and Some Remarks
A tree axiom.
A weakening of , with applications to topology
Addendum to “On Meager Additive and Null Additive Sets in the Cantor space and in ℝ” (Bull. Polish Acad. Sci. Math. 57 (2009), 91-99)
We prove in ZFC that there is a set and a surjective function H: A → ⟨0,1⟩ such that for every null additive set X ⊆ ⟨0,1), is null additive in . This settles in the affirmative a question of T. Bartoszyński.
Additive properties and uniformly completely Ramsey sets
We prove some properties of uniformly completely Ramsey null sets (for example, every hereditarily Menger set is uniformly completely Ramsey null).
Almost disjoint families: An application to linear algebra.